Feature space

A feature space is a mathematical space that determines an object by its measured values ​​in terms of its particular characteristics or features.

In the context of artificial intelligence is the term used in the pattern recognition.

In the empirical research, the term is used to classify measurement results and control the classification or type of education methodically.

In the artificial intelligence

The pattern recognition studied the automatic classification, ie how to classify objects into classes automatically. In order to distinguish objects, one first determines a set of characteristics in which they differ as much as possible. Then to measure these characteristics of each object to be classified, and writes the measurement results to each other in a vector, the so-called feature vector. This gives for each object a vector with as many entries as characteristics are considered. Each vector represents a point in the feature space; So, the feature space has as many dimensions as characteristics are considered. Wanted is now a function that divides the feature space into several classes, called a classifier.

Types of feature spaces

In the Pattern Recognition common feature spaces are multi-dimensional real vector spaces:

The dimension d of the space corresponds to the number of the examined features and can be very large.

In the empirical social research

The idea of ​​the feature space (English property- space) has been introduced by Paul F. Lazarsfeld in the methodology of empirical social research.

As in the ordinary conception of space, certain spatial coordinates are attributed in any place, so every object of study in social research can be assigned a number of feature dimensions, associated with each individual it can be attributed to a certain measurement value or a specific measurement category. The simplest type of feature is a dichotomous attribute. Unlike the usual notion of space more than three characteristics as well as different for each characteristic scale types can be used in the feature space. IBM used a long time for statistical analysis punch card contained 80 columns with 12 lines, which made it possible to classify each respondent to an opinion poll in a dichotomous attributes space of up to 960 forms.

The idea of ​​the feature space is particularly useful to reduce the data volume and to reduce it to a manageable number of classes or categories. You allowed this to control which reductions are theoretically and practically useful.

In addition, it serves to " substructure " of previously theoretically formed or encountered typologies. That is, a typology and their possibilities for classification are reviewed on the basis of the characteristics claimed for consistency and completeness. This can arise, that the list of specified features is inadequate and that it should be supplemented or reduced.